Modelling noisy data in a network context remains an unavoidable obstacle; fortunately, random matrix theory may comprehensively describe network environments effectively. Thus it necessitates the probabilistic characterisation of these networks (and accompanying noisy data) using matrix variate models. Denoising network data using a Bayes approach is not common in surveyed literature. This paper adopts the Bayesian viewpoint and introduces a new matrix variate t-model in a prior sense by relying on the matrix variate gamma distribution for the noise process, following the Gaussian graphical network for the cases when the normality assumption is violated. From a statistical learning viewpoint, such a theoretical consideration indubitably benefits the real-world comprehension of structures causing noisy data with network-based attributes as part of machine learning in data science. A full structural learning procedure is provided for calculating and approximating the resulting posterior of interest to assess the considered model's network centrality measures. Experiments with synthetic and real-world stock price data are performed not only to validate the proposed algorithm's capabilities but also to show that this model has wider flexibility than originally implied in Billio et al. (2021).

翻译：在网络环境中对噪声数据进行建模仍是一个不可避免的障碍；幸运的是，随机矩阵理论可以有效全面地描述网络环境。因此，有必要利用矩阵变量模型对这些网络（及其伴随的噪声数据）进行概率表征。在现有文献中，使用贝叶斯方法对网络数据进行去噪处理并不常见。本文采用贝叶斯视角，在正态性假设被违反的情况下，基于高斯图网络框架，通过引入矩阵变量伽马分布描述噪声过程，先验地提出了一种新型矩阵变量t模型。从统计学习角度看，这一理论考量无疑有助于在实际中理解由网络属性引发的噪声数据结构，这构成了数据科学中机器学习的一部分。本文提供了完整的结构学习流程，用于计算和近似所关注的后验分布，以评估所考虑模型的网络中心性度量。通过在合成数据与真实股票价格数据上的实验，不仅验证了所提算法的能力，还表明该模型比Billio等人（2021）最初所述具有更广泛的灵活性。